Problem: From a two-digit number N we subtract the number with the digits reversed and find that the result is a positive perfect cube. Then:
Answer Choices:
A. N cannot end in 5
B. N can end in any digit other than 5
C. N does not exist
D. there are exactly 7 values for N
E. there are exactly 10 values for N
Solution:
. Since both and lie between and cannot exceed . cannot exceed . The possible cubes are, therefore, , and , of which only is divisible by . so that the possibilities for are , seven in all.